On Affine-Scaling Interior-Point Newton Methods for Nonlinear Minimization with Bound Constraints

A class of new affine-scaling interior-point Newton-type methods are considered for the solution of optimization problems with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity o...

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Bibliographic Details
Published inComputational optimization and applications Vol. 35; no. 2; pp. 177 - 197
Main Authors Kanzow, Christian, Klug, Andreas
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.10.2006
Subjects
Applied mathematics
Mathematical programming
Methods
Optimization
Studies
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Summary:A class of new affine-scaling interior-point Newton-type methods are considered for the solution of optimization problems with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity of the solution. The new methods differ from previous ones by Coleman and Li [Mathematical Programming, 67 (1994), pp. 189-224] and Heinkenschloss, Ulbrich, and Ulbrich [Mathematical Programming, 86 (1999), pp. 615-635] mainly in the choice of the scaling matrix. The scaling matrices used here have stronger smoothness properties and allow the application of standard results from non smooth analysis in order to obtain a relatively short and elegant local convergence result. An important tool for the definition of the new scaling matrices is the correct identification of the degenerate indices. Some illustrative numerical results with a comparison of the different scaling techniques are also included.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-006-6514-5